The homotopy analysis method for multiple solutions of nonlinear boundary value problems

This paper investigates two basic steps of the homotopy analysis method (HAM) when applied to nonlinear boundary value problems of the chemical reaction kinetics, namely (1) the prediction and (2) the effective calculation of multiple solutions. To be specific, the approach is applied to the dual solutions   of an exactly solvable reaction-diffusion model for porous catalysts with apparent reaction order n=-1n=-1. It is shown that (i) the auxiliary parameter ℏ which controls the convergence of the HAM solutions in general plays a basic role also in the prediction of dual solutions, and (ii) the dual solutions can be calculated by starting the HAM-algorithm with one and the same initial guess. It is conjectured that the features (1) and (2) hold generally in use of HAM to identify and to determine the multiple solutions of nonlinear boundary value problems.